Fung Ho Tak. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2002. / Includes bibliographical references (leaves 107-110). / Text in English; abstracts in English and Chinese. / Fung Ho Tak. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Introduction to Geometric phase --- p.1 / Chapter 1.2 --- Introduction to Bose Einstein Condensation --- p.3 / Chapter 1.3 --- Motivation --- p.4 / Chapter 2 --- Review on Geometric phase --- p.6 / Chapter 2.1 --- Geometric phase achieved by undergoing adiabatic cyclic evolution --- p.7 / Chapter 2.2 --- Geometric phase acquired by undergoing cyclic evolution --- p.10 / Chapter 2.3 --- Geometric phase acquired by undergoing any evolution --- p.13 / Chapter 2.4 --- Geometrical representation of a two-level system --- p.15 / Chapter 3 --- Geometric Phase in Physical Systems --- p.17 / Chapter 3.1 --- Aharonov-Bohm Effect --- p.18 / Chapter 3.2 --- An Electron in a Magnetic Field --- p.20 / Chapter 3.2.1 --- The geometric phase β0(t) --- p.23 / Chapter 3.2.2 --- The geometric phase β1(t) --- p.28 / Chapter 3.3 --- Geometrical picture of the two-level quantum system --- p.32 / Chapter 3.3.1 --- Geometrical interpretation of β0(t) --- p.33 / Chapter 3.3.2 --- Geometrical interpretation of β1(t) --- p.36 / Chapter 3.4 --- Summary --- p.37 / Chapter 4 --- Geometric phase of a particle in a vibrating cavity --- p.39 / Chapter 4.1 --- Energy of a particle in a vibrating spherical cavity --- p.40 / Chapter 4.2 --- Geometric phase of a particle in a vibrating spherical cavity --- p.43 / Chapter 4.2.1 --- β0(t) of a particle in a vibrating cavity --- p.44 / Chapter 4.2.2 --- β1(t) of a particle in a vibrating cavity --- p.46 / Chapter 4.3 --- The Rotating-Wave Approximation approach --- p.46 / Chapter 4.3.1 --- Energy of the particle by using RWA --- p.49 / Chapter 4.3.2 --- Geometric phase of the particle by RWA --- p.50 / Chapter 4.4 --- The SU(2) Method --- p.52 / Chapter 4.5 --- Summary --- p.53 / Chapter 5 --- Review on Bose Einstein Condensation --- p.55 / Chapter 6 --- Energies and wavefunctions of a condensate --- p.63 / Chapter 6.1 --- perturbation approach to solve the nonlinear Schrodinger equation --- p.63 / Chapter 6.2 --- Energy of a BEC in an oscillating harmonic trap --- p.66 / Chapter 6.3 --- Wavefunction of the condensate in a vibrating harmonic trap --- p.72 / Chapter 6.4 --- Energies and wavefunctions of SHO --- p.76 / Chapter 6.5 --- Summary --- p.78 / Chapter 7 --- "(δr)2,(δpr)2 and geometric phase of a condensate" --- p.79 / Chapter 7.1 --- Uncertainties in position and momentum --- p.80 / Chapter 7.1.1 --- (δr)2 and (δpr)2 for a BEC in an oscillating trap --- p.80 / Chapter 7.1.2 --- (δr) and (δpr) in a oscillating SHO --- p.85 / Chapter 7.2 --- Geometric phase of BEC --- p.85 / Chapter 7.2.1 --- β0(t) of BEC --- p.87 / Chapter 7.2.2 --- β1(t)of BEC --- p.90 / Chapter 7.3 --- Summary --- p.92 / Chapter 8 --- Summary --- p.95 / Chapter A --- Parameter space and Berry's phase for degenerate Hamilto- nian --- p.99 / Chapter B --- Dirac Phase Factor --- p.101 / Chapter C --- Hamiltonian of a frequency-varying harmonics oscillator --- p.104 / Bibliography --- p.107
| Identifer | oai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_323834 |
| Date | January 2002 |
| Contributors | Fung, Ho Tak., Chinese University of Hong Kong Graduate School. Division of Physics. |
| Source Sets | The Chinese University of Hong Kong |
| Language | English, Chinese |
| Detected Language | English |
| Type | Text, bibliography |
| Format | print, xi, 110 leaves : ill. ; 30 cm. |
| Rights | Use of this resource is governed by the terms and conditions of the Creative Commons “Attribution-NonCommercial-NoDerivatives 4.0 International” License (http://creativecommons.org/licenses/by-nc-nd/4.0/) |
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